MSCI 212 Statistical Methods for Business
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2025-2026 COURSEWORK
PART II (Second, Third and Final Year)
MANAGEMENT SCIENCE
MSCI 212 Statistical Methods for Business
WRITTEN COURSEWORK ASSIGNMENT (DUE WEEK 12)
Please read the following instructions carefully.
1. Your coursework must be submitted electronically to the MSCI212 Moodle site as a single document (PDF only) by 10:00am on Monday, 19th January 2026. The place to submit your file is in the Coursework section of the MSCI212 Moodle site. Page Limit: 10 pages.
2. You are expected to have read and understood the University regulations relating to plagiarism. Plagiarism includes:
• Collusion, where a piece of work prepared by a group is represented as if it were the student’s own;
• The purchase of a paper from a commercial service, including Internet sites, whether pre-written or specially prepared for the student concerned;
• The submission of a paper written by any other person, including a friend, a fellow student or a person who is not a member of the university;
• The submission of another student’s work, whether with or without that other student’s knowledge or consent.
Incidents of plagiarism are recorded on a student’s file. Penalties are in line with the institutional framework of the University.
3. Generative AI category: AMBER. Coursework with AMBER means that Gen AI tools can be used in an assistive role. You also need to acknowledge the use of Gen AI tools. Please refer to the following link for acknowledging the use of Gen AI: https://portal.lancaster.ac.uk/ask/university-position-ai/.
4. In accordance with University regulations, marks are deducted from any coursework which is not submitted by the deadline. This penalty will apply for 3 days after the deadline and then a mark of zero will be given to any work not submitted. However, if an extension is given then the rule applies from the date of the extension.
5. Each of your answers should state your reasonings clearly. Please also state any assumptions that you have made in addition to those given in the questions.
6. You are allowed to submit handwritten answers but should include carefully selected extracts of your SPSS output to justify your answers. Also, please write neatly and if we cannot read your handwriting your answer will NOT be marked.
Tasks [Worth 100% of the marks]
You are a business analyst at a UK-based venture capitalist. Your manager needs a regression model that serves two main purposes: (1) assessing factors that are contributing to the profit, and (2) predicting the profit based on available information. It is known that how a start-up spends its money affects its profit. In particular, we are looking at the research and development, the administration, and the marketing spending of the listed start-up companies.
Based on this information, you are asked to develop a regression model. You need to assess the relationship between each spending post and the profit. You also need to use the model to predict the profit of three start-up companies. The dataset is already prepared (see file Startups.sav, adapted from kaggle.com). The data description (in thousands GBP) is as follows:
• Profit – profit of each company;
• RDSpend – spending on research and development of the company’s products;
• AdminSpend – spending on the administration of running the company;
• MarketingSpend – spending on marketing activities of the company for all products.
You need to write a technical report for your manager. Note that your manager has some knowl- edge of business statistics, and it is important to present the statistical outputs as clearly and simply as possible. The quality of the report is worth 5 marks. Follow the suggested formats (at the end of the coursework brief) for guidance in writing the report.
1. Preliminary analysis [20 marks]
(a) Carry out a preliminary analysis of the data using scatterplots, and comment on the relationships between the dependent and the explanatory variables and between the explanatory variables.
(b) Extend the analysis in (a) using a correlation matrix. Comment on the relationships between the variables and whether the findings in (a) and (b) are consistent.
2. Modelling [30 marks]
(a) Use stepwise regression starting with a “no-variable” model and identify “the best” model based on your results in (2.a). Justify your answer.
(b) Repeat (2.a) but use stepwise regression starting with an “all-in variable” model. Identify the “best” model based on your results in (2.b). Justify your answer.
(c) Based on your answers to (2.a) and (2.b), compare and discuss which model is the best. Write down your final/preferred model as an equation. Interpret the coefficients of the final model.
3. Residual diagnostics [20 marks]
Based on your final model in (2.c), save the residuals of the model and assess whether they follow the assumptions of errors in a linear regression model.
(a) Plot a histogram of the residuals. Comment on any observations about the histogram.
(b) Conduct tests for normality on the residuals. Interpret your results.
(c) Plot your residuals with each explanatory variable and the predicted values. Comment on each relationship.
(d) Summarise your findings on the residual diagnostics and compare them with the error assumptions of a linear regression model.
4. Predictions [10 marks]
Your company received three funding proposals from three different start-up companies. Each of them provides you with the research and development, the administration, and the marketing spending. They also provide their expected profits so that you can compare your predictions with theirs. The spending items and the expected profits are stated in the table below.
|
Company |
RDSpend |
AdminSpend |
MarketingSpend |
ExpectedProfit |
|
A |
29.62 |
115.82 |
297.11 |
49.49 |
|
B |
108.29 |
153.51 |
0 |
122.78 |
|
C |
62.76 |
127.61 |
353.18 |
105.01 |
(a) Use your final model, assuming that your model is valid:
i. to produce point predictions.
ii. to produce the 95% confidence intervals.
iii. to produce 95% prediction intervals.
(b) Comment on the predictions, taking into consideration the results of residual diagnostics and the descriptive statistics of your data.
5. Discussion [15 marks]
(a) Comment on the difference between your predictions and theirs, i.e., whether each company is overestimating or underestimating their performance.
(b) If you are responsible for selecting which companies would be funded, which companies would you select and why?
Advice for writing a technical report:
1. The page limit is 10 pages. Reports longer than 10 pages will be subject to penalties.
2. A suggested template in a Word document is available on Moodle. We encourage students to use the suggested template for marking purposes. Write your findings in paragraphs.
3. You should use the headings of the task (Preliminary analysis, Modelling, etc) as your head- ings for your report.
4. You should add a number and a caption for each table and figure. Each caption needs to be meaningful and summarise what the table/ figure shows in a sentence. Remember to put page numbers.
5. You should write the Conclusion at the end of the report. The conclusion must include:
(a) a short description of the problem;
(b) your approach to solving the problem;
(c) your recommendations.
Write a maximum of 5 sentences for the Conclusion. This will be assessed.
2026-01-14